Journal
JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS
Volume 10, Issue 6, Pages 3328-3343Publisher
INT SCIENTIFIC RESEARCH PUBLICATIONS
DOI: 10.22436/jnsa.010.06.42
Keywords
Dirac integrable hierarchy; integrable coupling; Hamiltonian operator; Magri pattern; bi-Hamiltonian structure; Darboux transformation
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Funding
- Nature Science Foundation of Shandong Province of China [ZR2014AM001]
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An integrable coupling hierarchy of Dirac integrable hierarchy is presented by means of zero curvature representation. A Hamiltonian operator involving two parameters is introduced, and it is used to derive a pair of Hamiltonian operators. A bi-Hamiltonian structure of the obtained integrable coupling hierarchy is constructed with the aid of Magri pattern of bi-Hamiltonian formulation. Moreover, we prove the Liouville integrability of the obtained integrable coupling hierarchy and establish a Darboux transformation of the integrable coupling. As an application, an exact solution of the integrable coupling of Dirac equation is given. (C) 2017 All rights reserved.
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